Basic asymptotic estimates for powers of Wallis ratios

For any a is an element of R, for every n is an element of N, and for n-th Wallis ratio w(n) := Pi(n)(k=1) 2k-1/2k, the relative error r(0) (a, n) := (v(0()a, n) - w(n)(a))/w(n)(a) of the approximation w(n)(a) approximate to v(0) (a, n) := (pi n)(-a/2) is estimated as vertical bar r(0) (a, n)vertical bar < 1/4n. The improvement w(n)(a) approximate to v(a, n) :=(-a/2) (1 - a/8n + a(2)/128n(2)) is also studied.